Mak, Richard (2019) The generating series of a walk in the quarter plane. Master's Thesis / Essay, Mathematics.
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Abstract
We consider walks with short steps in the quarter plane, that is, walks starting at (0, 0) that take steps from a fixed subset of {(0, 1),(1, 1),(1, 0),(1, −1),(0, −1), (−1, −1),(−1, 0),(−1, 1)}. The walk being in the quarter plane means that no intermediate point has a negative coordinate. Combining previous works on this subject, we examine the problem of calculating the number of ways one can get from (0, 0) to (i, j) in k steps by examining the generating series associated to the walk. We apply existing theory to more quickly determine the size of a certain invariant of the walk called its group, by using the theory of elliptic surfaces. Many examples will illustrate the theory.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Top, J. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 15 Jul 2019 |
| Last Modified: | 16 Jul 2019 11:52 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/20221 |
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